Question

find the smallest number by which 280
must be divided to make it a perfect
square ​ ​

Answer 1

Smallest number by which 280 must be divided to make it a perfect square

Explanation -
___________

Take the HCF of 280

=> 2 × 2 × 2 × 7 × 5

Make pairs from these and take out the left numbers

=> 2 × 7 × 5 ( are the left numbers )

So we should divide 280 by 2 × 7 × 5 = 70 to make it a perfect square.

=> 280 ÷ 70 = 4

=> 4 which is a perfect square

Answer 2

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♦ Before finding out the smallest number by with 280 must be divided to make it perfect square we must know

• What is a square ?

>> The multiplication of number by its own is Square .

• What are factors ?

>> The numbers from which the number is divisible.

• What is prime factorization ?

>> Breaking of number in the form of its prime factors

♦ Solving the problem :-

• Prime factorization of 280

02|280

02|140

02|70

05|35

07|7

01|1

So prime factorization = 2 × 2 × 2 × 5 × 7

Now as square root = number multiplied by itself.

=> The required number from above

= 2 × 2

Then The numbers remaining after finding out the square = 2 × 5 × 7

So the number from which we should divided 280 to make it a perfect square

= 2 × 5 × 7

= 70